Finite Group DatabasebetaFinite Group Databasebeta| order | 17914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D53⋊C169 |
| unambiguous semidirect product | (C53⋊C169)⋊C2 |
| derived, Sylow | C53 ⋊ C2×C169 |
| Hall | C53⋊C169 ⋊ C2 |
| Hall | D53 ⋊ C169 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C13 | D53⋊C13 |
| commutator, hypocenter | C53 | C2×C169 |
| Fitting, socle, cosocle | C13×C53 | C2×C13 |
| prime radical | C13×D53 | C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C13 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8957 |
Polycyclic presentation:
2,13,53,13|b^13=d,c^a=c^52,c^b=c^16364 conjugacy classes — view the full character table.
| maximal subgroup of | #6157⋊C169, C2×D53⋊C169 |
| maximal normal subgroup of | #6157⋊C169, C2×D53⋊C169 |
| maximal quotient of | Dic53⋊C169, C2×D53⋊C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17914, 2);